Chaotic advection mixer for capturing transient states of diverse biological macromolecular systems with time-resolved small-angle X-ray scattering

A chaotic advection mixer is employed to expand the range of reactions that can be probed with time-resolved solution scattering.

1. Valves are switched to the 'load' position.
2. Syringes are connected to the load valve with a needle port and both the buffer and sample loops for each side of the mixer are filled.
3. Valves are switched to the 'run' position for the buffer, and the syringe pumps are turned on to start pushing oil to drive the buffers into the mixer. The flowrate of the oil and the total flow rate through the mixer are monitored with flow meters.
4. Once the total flowrate has reached the target value, data collection begins for the 'pre-buffer'. 11. The loops are then cleaned with soap and water and dried with nitrogen gas so that they are ready for the next sample. At the same time, the oil syringes are refilled through an automated process.
There are many benefits to this loop loading setup, namely that high quality data can be achieved while still conserving samples and performing experiments in a timely manner. To ensure good data quality, this scheme allows for accurate buffer subtraction by producing a repeatable path length for sample and buffer scans. The sample and buffer species are driven by the same syringe pump, so the same conditions are reached for both sample and buffer scans, which is key for a good match.
Additionally, using an immiscible oil to drive the species out of the loops prevents sample dilution, therefore a constant concentration of sample is maintained throughout the measurement. To reduce sample consumption, the loops are dried with nitrogen gas as part of the cleaning cycle, which removes the need to flush the loops when loading and further prevents sample dilution. Also, the loops are positioned as close to the sample cell as possible, which cuts down on dead volume. The loops are easy to load, and it is recommended that several (3-5) excess µL of sample and buffer are loaded to ensure that any bubbles introduced while making the needle port connection are flushed backwards through the loop and out into the waste. To guarantee speedy data acquisition, the system was designed to reach stable, repeatable flowrates as efficiently as possible. Specifically, the overall volume of the oil syringes is kept low (100-250 μL), which allows for target flowrates to be reached quickly. With the automatic refill system, the syringes are simply refilled between datasets. Also, all downstream fluidic components have small inner diameters and there are no O-rings or soft tubing that would cause major pressure fluctuations or impact the overall flow stability. All components were carefully considered to keep flow stability and efficiency as top priorities. Lastly, the loop-loading system is also a highly flexible platform. Static measurements can easily be accommodated with minimal setup changes, allowing for easy comparison between static and time-resolved data within the same beamtime and under the same conditions. If desired, a manual approach, in which the samples and buffers are directly loaded into syringes, is also possible, but can be challenging. Stainless steel high-pressure syringes should be used to withstand the pressure caused by the higher flow rates and small inner diameter (75-100 micron) of the tubing connected to the sample cell. These syringes typically have a large volume (5-10 mL), so a lot of sample needs to be loaded at once, which is not ideal for purified proteins and some ligands that are available in limited quantities. These syringes can also be slow to pressurize when initiating the syringe pump. Additionally, when switching between samples or different conditions, the syringes need to be manually removed from the pumps, cleaned, and then refilled, which can be very time consuming when trying to collect multiple time series. Lastly, this system had a higher dead volume as the sample had to travel from the syringe, through the switching valve, and then finally to the mixer. Figure S2 shows a second Kenics design, with a straight opening. The tip is 150 μm in diameter, so when the stream exits the insert, it still needs to expand to its full 250 μm diameter. The channel with the Kenics mixing elements is also 150 μm diameter ( Figure S2E), which is slightly larger than the 100 μm diameter in the cone opening design. Additionally, there are only 5 elements in this mixer, as opposed to the 8 in the cone opening design. Although both the wider channel and fewer elements IUCrJ (2023). 10, https://doi.org/10.1107/S2052252523003482 Supporting information, sup-4 result in slightly slower mixing, it can still be successfully used. The 5 elements in a 150 μm channel produce ~2000 nm thick layers.

S2.2.1 Supply Line Binding Details
Two, ~24" long capillary tubes with 75-100 µm inner diameter and 200 µm outer diameter (TSP100200, Polymicro Technologies, Phoenix, AZ) were inserted into the ports on the Kenics mixer with a three-axis translation stage. Next a sub microliter amount of UV curable epoxy (UV18S, Masterbond, Hackensack, NJ) is applied onto the gap between the two supply lines just behind the insert. When the epoxy bridged the two supply lines, the applicator was used to carefully draw it forward until it reached the back of the insert, where it could wick into the supply line ports. This application method was chosen because it gave a large amount of control and ensured the epoxy did not flow onto the outside of the insert or form a large blob that would have interfered with the passage of the sheath flow. When the epoxy had wicked to the bottom of the ports, it was rapidly cured from both sides with light from a 365 nm LED (LED Engin Inc., Marblehead, MA). Figure S3A shows a picture of a mixing insert with supply lines bonded in. In subsequent mixer assembly steps, a seal must be made around these two supply lines using a single standard microfluidic port. To accomplish this, both supply lines were encapsulated by a larger glass tube, around which the seal can be made ( Figure S3b). A 20 mm long piece of 550 µm ID, 794 µm OD glass tubing (Drummond Scientific, Broomall, PA) was placed over the supply lines so that its closest end was 25 mm upstream of the mixing insert. Low viscosity UV curable epoxy (UV15, Master Bond) was wicked through the glass tube and cured. Cartoon illustrating the bonding of the larger glass tube (light blue) over the supply lines to create a single seal. Epoxy is shown in purple. The large glass is positioned much further away from the insert than illustrated here.

S2.2.2 Surface Treatment for Reducing Insert Hydrophobicity
The epoxy-like material that the insert is made of is naturally hydrophobic. As a result, air bubbles inside of the insert are challenging to displace, and bubbles in the Kenics elements can interfere with mixing. Therefore, a surface treatment that renders the inserts less hydrophobic is beneficial. A modified version of a treatment often used for microfluidic devices made from SU-8 (Sobiesierski et al., 2015;Wang et al., 2005) works well for these inserts.
The surface treatment must be performed after the supply lines are glued into the insert. The first step is to use ceric ammonium nitrate (CAN) to catalyse a reaction in which nitric acid breaks open the epoxy rings on the surface of the insert. For the treatment to be effective, no bubbles can be present in the interior of the insert so that the chemical can access all of its interior surfaces. This was achieved by flowing water through each of the supply lines and the insert and then placing the insert in a sonicator for 10-20 s.
The insert was then quickly transferred to a beaker of 0.1 M ceric ammonium nitrate (CAN) in1 M nitric acid held at 50° C. During the transfer, water flow was kept on preventing air from re-entering the insert. Once the insert was submerged in the CAN mixture, the syringe pump was set to withdraw fluid through the insert at 5 µL/min on each line. This ensured that fresh CAN mixture was always circulating through the insert to react with the interior surfaces. This process was allowed to continue for 50 minutes. At this point, the color of the insert changes from yellow to green.
After the CAN treatment, the insert was thoroughly rinsed with distilled water to remove CAN from the supply lines and interior channels. This was crucial because the CAN mixture is insoluble in the chemical which forms the second stage of the treatment, so it must be thoroughly flushed out to avoid clogging. The same sonication step was repeated to remove any bubbles that entered the insert during cleaning, and then the insert was transferred directly to a beaker of 0.1 M ethanolamine in 0.1 M sodium phosphate buffer at 50° C. The syringes were set to withdraw the ethanolamine mixture through the insert at 5 µL/min for 20 minutes. After this, the insert was removed and thoroughly flushed with distilled water. The green color remained. After surface treatment, bubbles were readily flushed out of the device. A high flow rate of water or soap (~100 µL/min) through the insert can remove any bubbles that do not dislodge during normal operation.

S2.2.3 Sample Cell Fabrication
Each mixer was assembled with custom components and mount, shown in Figure S4   Supporting information, sup-7 mixing insert, and e) the tee that facilitates concentric flow of the sheath around the supply lines and insert.

S2.3 Mixing Times and Final Timepoint Probed
From the Navier-Stokes equations, the general solution for the flow velocity, , along the channel before applying boundary conditions is: where and are the flow velocities of the sheath and sample respectively, and are the viscosities of the sheath and sample respectively, is the pressure gradient along the z-axis (direction of flow; − ∕ ), and are the densities of the sheath and sample respectively, g is the acceleration due to gravity (Squires & Quake, 2005). After applying boundary conditions, the four constants are:

S3
Where is the radius of the sample cell and is the radius of the inner sample stream.
The volumetric flowrate, and , for the sheath and sample is calculated by radially integrating the velocity to get: The above represents the solution for the cone opening design. For the straight opening design, the final timepoint must be adjusted to also include the additional time it takes for the central sample stream to expand to its full width. Additionally, since the straight opening design only has five elements, it is only compatible with Reaction Classes 2 and 3.
The uncertainty in the timepoint has three main contributors: the transit time through the Kenics insert, the flow dispersion due to the parabolic flow profile in the observation region of the sample cell, and the travel time through the vertical height of the X-ray beam ("beam smearing"). Here, we approximate the uncertainty due to the transit time through the Kenics as half of the average transit time. We added the transit time uncertainty, the flow dispersion, and the beam smearing in quadrature to obtain the full uncertainty for each timepoint, similar to the approach taken in (Plumridge et al., 2018).

S2.4 Myoglobin and Azide: Straight Opening Results
Absorbance experiments were repeated with the straight opening Kenics device. Data acquired with 15 mM azide were recorded after the expansion region and showed single exponential behavior, with k = 2.3 x 10 3 M -1 s -1 . Additionally, the measured dead times (average of 5.5 ms for both devices), show that the sample was fully mixed before it transited half of the insert, demonstrating the effectiveness of the Kenics mixer design. Additionally, it is important to note that any build-up of debris in the mixer, due to impurities in the sample or lack of pre-filtering, or the introduction of bubbles can impede mixing, which was evident by data acquired that could not be fit by a single exponential (data not shown).

Time from Absorbance Data
For the reaction between myoglobin and azide, two states contribute to the absorbance: unbound myoglobin and bound myoglobin, referred to here as State A and State B. To calculate the absorbance during the reaction, the concentrations, and , and extinction coefficients, and , for both states must be included. Therefore, for this system the intensity, , at each position is Here, is the path length. Since all the molecules start out in State A, is just the total concentration, , minus the concentration of molecules currently in State A. Therefore, we can rewrite equation S1 as = 10 (( ) ) . S7 If this intensity of the reacting sample, ( ), is divided by the intensity of the unreacted myoglobin sample, ( = 0), we get

S8
After simplification and taking the log, we get which can be converted to absorbance to give Since the azide concentration is in great excess of the myoglobin concentration, we can use standard pseudo-first order chemical reaction equations to express ⁄ as an exponential function, ( ) ⁄ , where represents time, is the dead time, or the time between the beginning of the reaction and the beginning of observation, and is the time constant of the reaction, which is directly proportional to the rate constant, k. Therefore, we can rewrite Equation S10 as = −log ( ) ( = 0) = ( − ) (1 − ( ) ⁄ ) S11

S2.4 Trypsin and Aprotinin: Assessment of Reproducibility
The reproducibility of measurements made with the chaotic advection mixer was assessed in two ways. In the first test, a 32 ms timepoint was probed, then the mixer was repositioned, and a different timepoint measured. Then, the mixer was returned to its original location so that the first timepoint could be probed again. This test yielded the repeatable profiles shown in Figure S5a. In the second test, both the flow rate and distance along the channel were adjusted to the same timepoint at two different conditions. These profiles also agreed well and are shown in Figure S5b. These tests demonstrate that the mixer produces robust, repeatable results over the course of an experiment and across a range of flow rates. Figure S5c-d show the Kratky plots of the full time series for comparison and to demonstrate that the 32 ms has a distinct profile.